An Equation of a Circle

An equation of any shape graphed in the xy-coordinate plane is a statement about all the points on it, using x and y as the coordinates.  If you have a circle of radius 5 centered at the origin, the Pythagorean Theorem tells us something that must be true of all points on the circle:

 

In general, the equation of a circle of radius r centered at the origin is:

 

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